I read and apply the Bible literally, yes. But that is not to say I take everything in wooden literal sense. For example if I suggested that it was raining cats and dogs outside, would you suppose that there are actually cats and dogs falling out of the sky?
I don't think that anyone can read and fully understand, in depth, the Bible just by picking it up. Yes, you can understand the basic tenants which are necessary for a relationship with God i.e. Creation, Immaculate Conception, Justification, Salvation, etc... However, to really understand the Bible you have to perfect the art and science of Biblical interpretation. You have to recognise several things to do this, the context in which the text is written, to whom the passage was written, the history involved, cultural issues, idiomatic differences, I could go on. People study the Bible for years just to understand it. The Bible is studied more than any other book in history. Consider any clergy member; my Pastor for instance has his undergrad in Theology, a Masters of Divinity, and a Phd. in Theology. That is 8 years of formal education, not to mention his daily and weekly study. All this education for one book. While he can answer most questions asked, he can't answer them all. There is just so much there.
So to address your question, I believe fully in the infallibility of the Bible. I believe it is the living breathing literal Word of God. There are gray areas in the Bible, however these are limited only by my own lack of knowledge, such as this issue.